I solved this absolute value equation and I am confuse about the answer given in the book for this question, the answer in the book is x > = 0 or x = -2/3 please tell me how can I get this answer from the following solution. Please tell the method which should be true for all such type of questions.

Attachment 18693

solving the second part we come to know that the right part of this is also true for all real numbers.

Please help.